Abstract
Consider a system operating as an M/M/c queue, where c=1, 1<c<∞, or c=∞. The system as a whole suffers occasionally a disastrous breakdown, upon which all present customers (waiting and served) are cleared from the system and lost. A repair process then starts immediately. When the system is down, inoperative, and undergoing a repair process, new arrivals become impatient: each individual customer, upon arrival, activates a random-duration timer. If the timer expires before the system is repaired, the customer abandons the queue never to return. We analyze this model and derive various quality of service measures: mean sojourn time of a served customer; proportion of customers served; rate of lost customers due to disasters; and rate of abandonments due to impatience.
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Yechiali, U. Queues with system disasters and impatient customers when system is down. Queueing Syst 56, 195–202 (2007). https://doi.org/10.1007/s11134-007-9031-z
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DOI: https://doi.org/10.1007/s11134-007-9031-z
Keywords
- Queues
- M/M/1
- M/M/c
- M/M/∞
- Failures
- Disasters
- Catastrophes
- Clearing
- Flushing
- Impatience
- Abandonments
- Sojourn times
- Quality of service